一种快速模拟振荡叶栅非定常流的数值方法

摘要

A harmonic balance method for the analysis of nonlinear unsteady flow around oscillating cas-cades is developed to improve computational efficiency for the simulation of periodic flow in turbomachinery. The periodic unsteady flow parameters can be represented by a Fourier series.In this way,the unsteady problem can be solved using conventional computational fluid dynamic method for steady problem.The anal-ysis exploits the fact that,calculated results by harmonic balance are in good agreement with those from du-al-time stepping method and linear method,and present method is highly efficient;it is about one order of magnitude faster than conventional dual-time stepping method in the present computation.The effects of the number of harmonics are also studied.It shows that lower order harmonic balance methods are sufficient to simulate periodic unsteady flow accurately except the flow fields including serious separated domain.So, lower order harmonic balance methods could be adopted to analysis unsteady flow in turbomachinery to re-duce the computational cost.In addition,the characteristic of unsteady flow around a compressor cascade is investigated,and the mechanism of generation of separated vortex and the vortex shedding frequency are also analyzed.%为了提高叶轮机内周期性非定常流数值计算效率，发展了一种计算振荡叶栅非线性非定常流的谐波平衡方法，将周期性非定常流动参数采用傅里叶级数表示，从而将传统的定常流动数值计算方法应用于非定常流问题求解中，大大提高了非定常流计算效率。计算结果表明，发展的谐波平衡方法与线性方法、非线性时域法计算结果吻合较好，且其计算效率比时域法高1个数量级。另外，系统研究了谐波阶次对计算效率与计算精度的影响，认为在气流未出现严重分离时，应采用低阶谐波平衡方法，以减少计算耗时。此外，从压气机振荡叶栅非定常流场计算结果可以看出，叶片吸力面诱导涡的生成频率与振荡频率并不一致，涡生成频率要高于振荡频率。